2023 AMC 8 Problems/Problem 6
Solution 1
First, let us consider the cases where is a base. This would result in the entire expression being
. However, if
is an exponent, we will get a value greater than
. As
is greater than
and
, the answer is
.
~MathFun1000
Solution 2
The maximum possible value of using the digit . We can maximize our value by keeping the
and
together in one power. (Biggest with biggest and smallest with smallest) This shows
=
=
. (Don't want
cause that's
) It is going to be
~apex304 (SohumUttamchandani, wuwang2002, TaeKim, Cxrupptedpat, stevens0209 (editing))